Object segmentation is a technique of recognising a shape or boundary of an object within a digital image. The aim of object segmentation is to change the representation of objects in an image (such as a medical image) so that the image is easier to analyse, for example, to determine whether an object has changed over time, from one image to another. There are many techniques that accomplish this object recognition which may be more or less appropriate depending on the range of contrast within the image, the extent of contrast between the object and the background, the scale or relative size of the object, the format of the image data, and so on. However, what most techniques have in common is that each pixel in an image (or voxel in a 3-D image) is assigned some sort of label corresponding to certain visual characteristics (such as grey scale, intensity, etc.). In this way, pixels (voxels) assigned a same or similar label may be seen by a viewer as being grouped together for some reason, for example to show that they are part of the same structure (e.g. the same object) in the image.
A type of object segmentation known as “blob detection” is described in T. Lindeberg's “Feature detection with automatic scale selection” in the International Journal of Computer Vision, Vol. 30, pp. 79-116, 1998. In this paper, a form of scale determination is described that uses a Laplacian operator of a Gaussian model (Laplacian-of-Gausian or LoG operator or filter) to determine relative positions and scales of “blobs” in an image.
A. Jirapatnakul, S. Fotin et al.'s “Automated Nodule Location and Size Estimation Using a Multi-scale Laplacian of Gaussian Filtering Approach” in the Annual International Conference of the IEEE EMBS, pp. 1028-1031, 2009 describes the application of Laplacian-of-Gaussian filtering from a starting point placed near the centre of a blob to find the size of the blob.
In both techniques mentioned above, an overall estimate of the scale of the blob is to be found using the LoG filter, which iteratively checks different scales (sigma values, to be described later) and finds one that is most likely to be the scale of the blob in question. In one dimension, the scale may be a distance from an origin to an estimated edge of the blob; in two dimensions, the scale may be a radius of a circle representing the blob and in three dimensions, the scale may be a radius of a sphere representing the blob. The scales determined by LoG filters are based on positions of change in contrast relative to a centre position. The change in contrast is assumed to be the edge of the blob. A “region-growing” approach analyses each pixel from a central point outwards, determining whether each pixel conforms to parameters used to identify an object. When pixels that do conform cease to be found, it is assumed that the positions at which the pixels cease to conform are positions corresponding to the edge of the object.
This process of “scale estimation”, which uses a LoG operation to estimate a scale of the object to be segmented, is a useful tool in object segmentation. For example, in the region-growing approach, scale estimation can be used to constrain an excessive region expansion (i.e. the process of analysing pixels increasingly outwards from the central point) because an approximate maximum size of the object is known (i.e. outside of a certain region found by scale estimation, pixels conforming to the parameters for inclusion in the object are unlikely to exist). However, there are potential problems in the scale estimation process. One of the problems is the risk of a very large computation time. In conventional scale estimation methods, such as those referred to above that use a LoG filter, the computation time is very large because the LoG filter is applied over a large processing range (i.e. over a large search space) and to every point therein. In general, scale estimation is an iterative process with changing parameters related to the number of points in the processing range and giving rise to a scale for each point. One then determines an appropriate scale from all computational results which, for a large processing range, may be many.
A next step in object segmentation processing (after the scale estimation step) may be the segmentation itself involving a region-growing method. From a central “seed” point, all points in a region of interest are analysed to determine whether they satisfy the criteria chosen to define the object. All points satisfying those criteria are determined to belong to the object.
An alternative segmentation process may be used. It may involve a level set algorithm as described in S. Osher and J. Sethian's “Fronts Propagating with Curvature-Dependent Speed: Algorithm Based on Hamilton-Jacobi Formulations” in the Journal of Computational Physics, Vol. 79, pp. 12-49, 1988 and in J. Sethian's “Level Set Methods and Fast Marching Methods” in the Cambridge University Press, 1999. These documents describe an algorithm that defines a front propagating with curvature-dependent speed. The way this is done is to take a surface, the “movement” (used as a time-dependent metaphor for variation over a dimension in space) of which is to be predicted, and to intersect it with a plane to define a contour. For example, a sphere may be bisected about its equator with a plane to define a circle on the plane. This contour (e.g. the circle) has a definable shape at time t=0 and in order to define how the contour changes over time (e.g. the diameter of the circle decreasing as the plane moves from the equator to a pole of the sphere), forces are applied to its “fronts” (e.g. its circumference) to define the direction in which the fronts will travel (e.g. inwards) as t changes.
In a case of a series of medical images such as computed tomography (CT) scans that combine to give a three-dimensional representation of an object in the human body for instance, the level set algorithm may be used to define the outer surface of the three-dimensional object. In order to do this, however, the edges of the object in all of the images making up the three-dimensional image must first be determined.
It is known to find the edges of the object using a segmentation process such as region-growing from a central seed point. From the central seed, an iterative process is applied to pixels surrounding the seed, going outwards until a pixel is reached that does not have the predefined parameters of the object (e.g. texture, colour, intensity, etc.) When several pixels are reached that are adjacent and that no longer satisfy the predetermined parameters, an edge of the object is presumed to have been reached. To build up the three-dimensional object shape, the region-growing process may be applied to multiple parallel images. The level set algorithm helps to reduce processing by reducing the need for a user to input a seed point in each image. It does this by using a limited number of object edges to build up the full 3-D shape.
One problem with these scale estimation and segmentation processes is that objects that are to be segmented, such as lymph nodes, are rarely perfectly spherical. Therefore, assumptions based on three-dimensional symmetry of a lymph node can cause large inaccuracies in the segmentation processes. For example, if a three-dimensional (3-D) LoG filter is applied to a lymph node that has different lengths in the three dimensions, the LoG filter is likely to estimate the scale of the lymph node as being a sphere with a radius equal to half of one of the lengths, that radius being dependent simply on which pixel-defined edge or LoG “peak” in a LoG output was found first in the iterative process or which “peak” was highest (peaks defining changes of pixel parameter and therefore likely edges of objects).
U.S. Pat. No. 7,333,644 describes the interpolation of a 3-D lesion surface into a surface representation in spherical coordinate space based on a centroid location of the lesion. Thus, the interpolation involves a transformation that changes the coordinates from Cartesian (x,y,z) into spherical r(φ,θ). This interpolation process is intended to render the sub-volume (including the lesion and its surrounding environment) isotropic, i.e., to make the dimensions of the pixels in the x-y slices the same as the dimensions of the pixels in the z-direction. This gives a slightly easier set of coordinates with which to work, but it does not deal with the problem of irregularly-shaped objects. The spherical coordinates cannot represent the position of each voxel without the fixed centroid because all parameters in the spherical coordinate depend on the centroid. Thus, processing remains laborious.